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An ideal gas, Cv=5/2R is expanded adiabatically against a constant pressure of 1atm untill it doubles in volume.If the initial temperature is 25degree celsius and the initial pressure is 5atm,the value of T2 is?
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An ideal gas, Cv=5/2R is expanded adiabatically against a constant pre...
Given
- Cv = 5/2R
- Adiabatic expansion
- Constant pressure = 1 atm
- Volume doubles
- Initial temperature = 25°C = 298K
- Initial pressure = 5 atm
Solution
Step 1: Finding initial volume and moles of gas
Using ideal gas equation, PV = nRT
Initial volume, V1 = nRT1/P1 = (1 mole x 5 atm x 298K) / 5 atm = 298 L
Number of moles, n = PV/RT = (5 atm x 298 L) / (0.082 L atm/K mol x 298 K) = 1.82 moles
Step 2: Finding final temperature and volume
Using adiabatic expansion equation, P1V1^γ = P2V2^γ where γ = Cp/Cv = 7/5 for ideal gas
Final volume, V2 = 2 x V1 = 596 L
Final pressure, P2 = P1(V1/V2)^γ = 5(1/2)^7/5 = 2.07 atm
Using ideal gas equation, P2V2 = nRT2
Final temperature, T2 = P2V2/nR = (2.07 atm x 596 L) / (1.82 mol x 0.082 L atm/K mol) = 638K
Answer
The final temperature, T2 = 638K.
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An ideal gas, Cv=5/2R is expanded adiabatically against a constant pressure of 1atm untill it doubles in volume.If the initial temperature is 25degree celsius and the initial pressure is 5atm,the value of T2 is?
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An ideal gas, Cv=5/2R is expanded adiabatically against a constant pressure of 1atm untill it doubles in volume.If the initial temperature is 25degree celsius and the initial pressure is 5atm,the value of T2 is? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about An ideal gas, Cv=5/2R is expanded adiabatically against a constant pressure of 1atm untill it doubles in volume.If the initial temperature is 25degree celsius and the initial pressure is 5atm,the value of T2 is? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ideal gas, Cv=5/2R is expanded adiabatically against a constant pressure of 1atm untill it doubles in volume.If the initial temperature is 25degree celsius and the initial pressure is 5atm,the value of T2 is?.
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